Parametric functional analysis of variance for fish biodiversity assessment

Due to the increasing impact of human activities, water conservation has become a primary aim of environmental management policies. In this context, fish biodiversity represents a good measure of water quality because changes in ecological factors involve qualitative modifications in species composition. For this reason, the analysis of the interaction between biodiversity and environmental characteristics becomes crucial. This paper aims to analyse the effects of habitat and seasonality on fish biodiversity in freshwater environments. In particular, we applied functional data analysis to the beta diversity profile. The proposed approach allows us to overcome the limitations of the classical biodiversity indices, highlighting its multidimensional aspect. More in detail, our research focuses on the functional data analysis of variance in order to quantify the effects exerted on a functional observation by some factors. This model is applied to a real data set concerning ichthyic biodiversity of 104 streams in the province of Arezzo (Central Italy). We consider first the fish zonation and then the seasonality as factors; the results show that species diversity fluctuates seasonally whereas the zonation has no significant effect in influencing the biodiversity. Our proposal is a powerful tool for the analysis of the relationship between qualitative variables and a functional response. Since the diversity profile is a function of the relative abundance vector in a fixed domain, this method is particularly suited to the beta profile and it could be very helpful to monitor or to identify areas of high environmental risk